Related papers: A statistical mechanics framework for constructing…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental…
The numerical investigation of the statics and dynamics of systems in nonequilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We briefly review the recently developed, Markov process based isothermal chemical thermodynamics for nonlinear, driven mesoscopic kinetic systems. Both the instantaneous Shannon entropy {\boldmath $S[p_{\alpha}(t)]$} and relative entropy…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory.…
Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are…
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
This paper reports on a macroscopic fluctuation theory developed over the last ten years in collaboration with L. Bertini, A. De Sole, D. Gabrielli and C. Landim. This theory has been inspired by and tested on stochastic models of…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…